Question

What is the value of b in the equation (y^b)^4 = 1/y^24?

Answer 1

Answer:

Step-by-step explanation:

Since we are solving an exponential equation so we first need to think about making the base of both sides of equation same .

$(y^b)^4 = 1/y^{24} )$

it simplifies to

$y^{4b} = 1/y^{24}$

$y^{4b} = y^{-24}$

Now base is same on both sides so we can equate the exponent

$4b=-24\\b=\frac{-24}{4} \\b=-6$

Answer 2

$\bf a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}}\\\\ -----------------------------\\\\ (y^b)^4=\cfrac{1}{y^{24}}\iff y^{b\cdot 4}=y^{-24}\implies y^{4b}=y^{-24} \\\\\\ \textit{bases are the same, exponents must be the same} \\\\\\ 4b=-24$

solve for "b"